As a presheaf category, the category of precubical sets is cocomplete, with
colimits being computed pointwise [1]}. In particular, we denote
by \(C\sqcup D\)  the coproduct of two cubical sets, and given a precubical set \(C\) 
and two 0-cubes \(c,d\in C(0)\) , we write \(Ccd\)  for the precubical set
obtained from \(C\)  by identifying \(c\)  and \(d\)  (this precubical set can be
obtained as the expected coequalizer). Finally, given a set \(X\subseteq C(0)\)  of
0-cubes of a precubical set \(C\) , we write \(C\setminus X\)  for the
precubical subset of \(C\)  consisting of \(n\) -cubes of \(C\)  which do not contain an element of \(X\)  as
iterated face.
